# Showing that there exists an algorithm, that converts NFA to DFA under some cirumstances

We are given NFA $A$, which for every input word $w$ has at most 10 runs over word $w$, beginning at the starting state. Show that there exists an algorithm, that converts such NFA to DFA in polynomial time. We don't need that algorithm to work if given automata is not such a NFA.

I think we need to construct DFA with $2^{10}$ states, such that every state would correspond to some run in the NFA - but im not sure about the details.

Any ideas?